Abstract
Consider the continuous map →: X → X and the continuous map \(\bar f\) of K(X) into itself induced by →, where X is a metric space and K(X) the space of all non-empty compact subsets of X endowed with the Hausdor. metric. According to the questions whether the chaoticity of → implies the chaoticity of \(\bar f\) posed by Román-Flores and when the chaoticity of → implies the chaoticity of \(\bar f\) posed by Fedeli, we investigate the relations between → and \(\bar f\) in the related dynamical properties such as transitivity, weakly mixing and mixing, etc. And by using the obtained results, we give the satisfied answers to Román-Flores's question and Fedeli's question.
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Liao, G., Wang, L. & Zhang, Y. Transitivity, mixing and chaos for a class of set-valued mappings. SCI CHINA SER A 49, 1–8 (2006). https://doi.org/10.1007/s11425-004-5234-5
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DOI: https://doi.org/10.1007/s11425-004-5234-5